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New results on embeddings of self-similar sets via renormalization
Amir Algom, Michael Hochman, Meng Wu
For self-similar sets , we obtain new results towards the affine embeddings conjecture of Feng-Huang-Rao (2014), and the equivalent weak intersections conj…
How linear can a non-linear hyperbolic IFS be?
Amir Algom, Snir Ben Ovadia, Federico Rodriguez Hertz +1
Motivated by a question of M. Hochman, we construct examples of hyperbolic IFSs on where linear and non-linear behaviour coexist. Namely, for every $2\leq r \leq \infty…
On the dimension of orthogonal projections of self-similar measures
Amir Algom, Pablo Shmerkin
Let be a self similar measure on , , and let be an orthogonal projection onto a -dimensional subspace. We formulate a criterion on the action of t…
Spectral gaps and Fourier decay for self-conformal measures in the plane
Amir Algom, Federico Rodriguez Hertz, Zhiren Wang
Let be a self-conformal IFS on the plane, satisfying some mild non-linearity and irreducibility conditions. We prove a uniform spectral gap estimate for the t…
Arbitrarily slow decay in the logarithmically averaged Sarnak conjecture
Amir Algom, Zhiren Wang
In 2017 Tao proposed a variant Sarnak's Möbius disjointness conjecture with logarithmic averaging: For any zero entropy dynamical system , $\frac{1}{\log N} \sum_{n=1} ^N \f…
Van der Corput and metric theorems for geometric progressions for self-similar measures
Amir Algom, Yuanyang Chang, Meng Wu +1
We prove a van der Corput lemma for non-atomic self-similar measures . As an application, we show that the correlations of all finite orders of conver…